This is an announcement for the paper "Approximation of operators in Banach spaces" by Oleg I. Reinov. Abstract: It is a translation of an old paper of mine. We describe the topology tau_p in the space Pi_p(Y,X), for which the closures of convex sets in tau_p and in *-weak topology of the space Pi_p(Y,X) are coincident. Thereafter, we investigate some properties of the space Pi_p, related to this new topology. 2010-remark: Occasionally, the topology is coincides with the lambda_p-topology from the paper "Compact operators which factor through subspaces of l_p", Math. Nachr. 281(2008), 412-423 by Deba Prasad Sinha and Anil Kumar Karn. Archive classification: math.FA Mathematics Subject Classification: 46B28 Citation: In the collection "Primenenie funkcional'nogo analiza v teorii The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1002.3902 or http://arXiv.org/abs/1002.3902 or by email in unzipped form by transmitting an empty message with subject line uget 1002.3902 or in gzipped form by using subject line get 1002.3902 to: math@arXiv.org.